In 1964, Chance became at the time the youngest pitcher to win the Cy Young Award[3] when, as a member of the Los Angeles Angels, he led the American League in wins (20), innings pitched (278 ⅓) and earned run average (1.65—as of 2013, a franchise record) and was third in the A.L. in strikeouts.[1] He pitched 11 shutouts (also a franchise record as of 2013) that season, winning five of those by a 1–0 score.[1] At the time, only one Cy Young Award was given in all of MLB; since 1967, separate awards have been given in the AL and the National League.[4] Chance's Cy Young Award was the third in a string of five consecutive Cy Young Awards won by a pitcher from a Los Angeles-based team. The others were won by Dodger pitchers: Don Drysdale in 1962 and Sandy Koufax in 1963, 1965 and 1966.[4]

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Chance attended West Salem's Northwestern High School and starred on the baseball team and basketball teams (leading the team to a 1958 state title), but it would be baseball where Chance would shine. During his career, he set several state records which still stand including a 52–1 career record, 20 wins in a season, 32 straight wins, eight no-hitters in a season (in both his junior and senior years), and 17 no-hitters total. He also led the Huskies to the Class A state semifinals in 1958 and a championship in 1959 (and pitching every inning of every postseason tournament game).[5]

Chance had an outstanding rookie campaign in 1962, winning 14 games with an ERA of 2.96 and finishing tied for third in AL Rookie of the Year voting with Bernie Allen and Dick Radatz (behind fellow Angel Buck Rodgers and winner Tom Tresh). The 1962 campaign would be notable for the Angels as Chance and fellow phenom Bo Belinsky would team on both the mound and in the Hollywood social circles, much to the enjoyment of the Los Angeles beat writers and the consternation of manager Bill Rigney and the rest of the Angels' front office.[3] Although he would lose 18 games in 1963, he would finish with a 3.19 ERA in 248 innings.[1] The pair were inseparable and often roomed together, some saying so that the Angels' would only have to mind one bad room – at least when they were in their room after curfew (which wasn't often).[3] After his 1964 season in which he won the Cy Young Award and was elected to his first All-Star Game, Chance would go 15–10 in 1965 and 12–17 record in 1966, despite a respectable ERA of 3.08.[1] After the 1966 season, the Angels, a weak hitting team desperate for power and looking to shed one of their problem children, shipped Chance and infielder Jackie Hernandez to the Minnesota Twins on December 2 in a trade that netted them outfielderJimmie Hall, slugging first basemanDon Mincher, and relief pitcher Pete Cimino.

Chance responded by winning 20 games for the Twins in 1967, leading the AL in games started (39), complete games (18) and innings pitched (283 ⅔).[1] On August 6 of that year, he pitched a rain-shortened, five-inning perfect game against the Red Sox at Metropolitan Stadium in Bloomington, Minnesota.[8] He also pitched a 2–1 no-hitter against the Cleveland Indians on August 25 with the Indians scoring their sole run in the first inning on two walks, an error, and a wild pitch.[9] Chance later said that umpire Ed Runge's wide strike zone had a lot to do with him keeping the Indians off the basepaths.[10] The Twins nearly won the 1967 pennant, but Chance was outdueled in the season's final game, at Fenway Park, by Boston's Jim Lonborg, chasing Chance in with 5 runs in the sixth despite getting only one ball out of the infield,[11] and the Red Sox emerged as surprise league champions — with Lonborg winning the 1967 AL Cy Young trophy in the process.[12] The trade helped both teams and Chance as the Angels rose to fifth place with an 84–77 record in 1967, the Twins were in it until the season's final game, and Chance was voted to his second all-star team and won the Sporting News AL Comeback Player of the Year award.[13]

The 1968 campaign saw Chance put up a lackluster 16–16 record (echoing the Twins' 79–83 finish), but saw him notch career lows in hits and walks per 9 innings (6.9 & 1.9 respectively), and career highs in innings (292), strikeouts (234), and strikeouts per 9 innings (7.9). Due to his strong numbers, Chance had more than a decent chance at again winning 20 games, but the Twins offense let him down in 1968, scoring two runs or fewer in 17 of his 22 starts (games in which Chance himself posted an ERA of 2.55). In the games in which the Twins scored at least three runs, Chance posted a 13–4 record.[14] Despite his strong season, owner Calvin Griffith, well known for being "thrifty", tried to cut Chance's salary by $9,000. Chance held out prior to the 1969 season and was successful in having his salary cut by "only" $5,000.[10] However, 1968 would be his last big year and Chance's career would rapidly decline. From 1969–1971, he would win a total of only 18 games. In 1969, Chance would be plagued by a back injury caused by rushing to get into shape following his holdout and only pitched 88 ⅓ innings. On December 10, 1969, the Twins would ship Chance, third baseman, and future New York Yankees star, Graig Nettles, infielder Ted Uhlaender, and pitcher Bob Miller to the Cleveland Indians for relief pitcher Stan Williams and future Boston Red Sox star Luis Tiant. The trade would end up being a disaster for the Twins as Nettles would immediately blossom and hit 26 home runs for the 1970 Indians and Tiant, the key to trade, would be released after only one injury-plagued season.

Chance would split the 1970 season between the Indians, for whom he'd pitch a 9–8 record with a 4.28, and the New York Mets (after being purchased from the Indians on September 18). Chance would be traded again on March 30, 1971, this time to the Detroit Tigers along with reliever Bill Denehy for minor league pitcher Jerry Robertson. Used largely out of the bullpen, Chance would finish his career with a 4–6 record in 31 games.

His career record over 11 seasons (1961–71) and 406 games pitched was 128 wins, 115 losses and an ERA of 2.92. He was a notoriously weak batsman in the days prior to the designated hitter, garnering only 44 hits in 662 at bats, for a batting average of .066. He struck out 420 times in those 662 at-bats.